A train 110 m long takes three seconds to pass a standing man. How long is the platform if the train passes through it in 15 seconds moving with the same speed?

Options

A. 440 m
B. 400 m
C. 550 m
D. 450 m

Answer

To solve the problem step by step, we will follow the same reasoning as in the video transcript.

### Step 1: Understand the problem
We know that a train is 110 meters long and takes 3 seconds to pass a standing man. We need to find out how long the platform is when the train passes through it in 15 seconds at the same speed.

### Step 2: Calculate the speed of the train
To find the speed of the train, we can use the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Here, the distance is the length of the train (110 meters) and the time is 3 seconds.

\[ \text{Speed} = \frac{110 \text{ m}}{3 \text{ s}} \]

Calculating this gives:
\[ \text{Speed} = \frac{110}{3} \text{ m/s} \]

### Step 3: Set up the equation for the platform
Let the length of the platform be \( x \) meters. The train takes 15 seconds to pass through the platform. The distance covered while passing the platform is the sum of the length of the train and the length of the platform.

The total distance covered when the train passes the platform is:
\[ \text{Distance} = \text{Length of Train} + \text{Length of Platform} = 110 + x \]

### Step 4: Use the speed to find the length of the platform
Using the speed we calculated earlier, we can set up the equation using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]

Substituting the known values:
\[ 110 + x = \left(\frac{110}{3}\right) \times 15 \]

### Step 5: Simplify the equation
Calculating the right side:
\[ 110 + x = \frac{110 \times 15}{3} \]
\[ 110 + x = \frac{1650}{3} \]
\[ 110 + x = 550 \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ x = 550 - 110 \]
\[ x = 440 \]

### Step 7: Conclusion
The length of the platform is \( 440 \) meters.